Question

The parent function, f(x)=5^x has been vertically compressed by a factor of one-half shifted to the right three units and down two units.
Choose the correct function to represent the transformation

Answer 1

Answer:

The required function is $g(x)=\frac{1}{2}(5^{x-3})-2$.

Step-by-step explanation:

The given parent function is

$f(x)=5^x$

The transformation of a parent function is defined as

$g(x)=kf(x+a)+b$

Where, k represents the vertical stretch or compression, a represents the horizontal shift and b represent the vertical shift.

→ If |k|>1, then it represents vertically stretch and If |k|<1, then it represent vertically compression.

→ If a>0, then f(x) shifts left by a units and If a<0, then f(x) shifts right by a units.

→If b>0, then f(x) shifts upward by b units and If b<0, then f(x) shifts downward by b units.

Since the graph of f(x) has been vertically compressed by a factor of one-half shifted to the right three units and down two units.

$k=\frac{1}{2}$

$a=-3$

$b=-2$

The graph of required function is

$g(x)=\frac{1}{2}f(x-3)-2$

$g(x)=\frac{1}{2}(5^{x-3})-2$

Therefore the required function is $g(x)=\frac{1}{2}(5^{x-3})-2$.